Apparatus and method for acoustic analysis of bone using optimized functions of spectral and temporal signal components

ABSTRACT

An apparatus and method determine externally in a vertebrate subject an index of porosity and non-connectivity of a bone. A preferred embodiment has first and second transducers and a mounting arrangement for mounting the transducers in spaced relationship with respect to the bone. A signal generator,in communication with the first transducer, causes the first transducer to produce acoustic signals, having energy distributed over a frequency range, that are propagated into the subject and received by the second transducer along a path the includes the bone. Finally, the embodiment has a signal processor, in communication with the second transducer, for providing a measurement that is a function of at least one of spectral or temporal components of the sisal received by the second transducer. The transducers act like a point source and point receiver.

The present application is a continuation in part of U.S. applicationSer. No. 08/404,813, filed Mar. 13, 1995 and now U.S. Pat. No.05,592,943, which is a continuation of U.S. application Ser. No.08/043,870, filed Apr. 7, 1993, issued on Mar. 14, 1995 as U.S. Pat. No.5,396,891; these related applications are hereby incorporated herein byreference.

TECHNICAL FIELD

The present invention relates to apparatus and methods for the acousticanalysis of bone, and more particularly to apparatus and methods foraccomplishing bone measurement using signal processing techniques.

BACKGROUND ART

The prior art is rich with approaches to measurement of bonecharacteristics using acoustic and other methods with a view toidentifying patients in need of treatment for osteoporosis. Manyacoustic techniques utilize a first transducer to provide an acousticsignal, typically at ultrasonic frequencies, to the subject from a firstexternal location and a second transducer at a second external locationdisposed on the opposite side of the bone of interest to receive thesignal transmitted by the first transducer through the bone andintervening soft tissue. (The transducers are typically coupled to thesubject through a suitable fluid, such as water.) Under one approach,there is determined the rate of Broadband Ultrasound Attenuation (BUA)in the range of approximately 300 to 700 kHz. The BUA is determined bymeasurement of the attenuation at a plurality of frequencies and thenfitting the measurements to a suitable linear logarithmic-amplitudeversus frequency scale. However, as an indicator of osteoporotic bone,BUA does not provide a desirable level of specificity and sensitivity.

SUMMARY OF THE INVENTION

The present invention provides, in some embodiments, enhancedspecificity and sensitivity in determining an index of porosity andnon-connectivity of a bone by utilizing a number of surprisingdiscoveries, including: (i) spectral estimation of a received ultrasoundsignal in bone is advantageously nonlinear and time variant; (ii)utilization of received signal information (such as phase) that is lostin BUA analysis permits more accurate assessment of bone condition;(iii) the use of transducers approximating a point source and a pointreceiver provide enhanced performance and flexibility in placement; and(iv) significant portions of the acoustic energy lost in attenuation indirect transmission through the bone can be measured by suitableplacement of a third transducer in a position distinct from the path ofdirect transmission.

In accordance with a preferred embodiment of the invention, there isprovided an apparatus for externally determining in a vertebrate subjectan index of porosity and non-connectivity of a bone. The embodiment hasfirst and second transducers and a mounting arrangement for mounting thetransducers in spaced relationship with respect to the bone. A signalgenerator, in communication with the first transducer, causes the firsttransducer to produce acoustic signals, having energy distributed over afrequency range, that are propagated into the subject and received bythe second transducer along a path that includes the bone. Finally, theembodiment has a signal processor, in communication with the secondtransducer, for providing a measurement that is a function of at leastone of spectral or temporal components of the signal received by thesecond transducer. The function is selected for its ability to minimizedifferences among successive measurements taken of the same individualand to maximize differences in measurements taken of differentindividuals, so that the measurement relates to the porosity andnon-connectivity of the bone. In a further embodiment, the function is aweighted sum of spectral components of the signal received by the secondtransducer, and the weights are selected for their ability to minimizedifferences among successive measurements taken of the same individualand to maximize differences in measurements taken of differentindividuals.

In related embodiments, the a signal processor provides a singlemeasurement that is a function of at least one of spectral or temporalcomponents of a portion, up to the whole amount thereof, of the signalreceived by the second transducer, such measurement being other than alog-linear slope estimation based on Fourier spectral information. In apreferred embodiment a selected one or both of the transducers employs avibrating element that is sufficiently small as to cause the selectedtransducer, if driven by the signal generator, to produce an acousticaloutput, into the body part, that is substantially like that of a pointsource. The function may include any or a combination of the following:

a weighted sum of spectral components of a portion of the signalreceived by the second transducer;

a measure of the shape of the Hilbert envelope of a portion of thesignal received by the second transducer;

a measure of the shape of anautoregressive moving average spectralestimation function of a portion of the signal received by the secondtransducer;

a measure of the variability of the Hilbert frequency function of aportion of the signal received by the second transducer;

a measure of the average Hilbert frequency function of an early portionof the signal received by the second transducer;

a weighted sum of spectral components, determined using a short-timeFourier transform, and determined at successive intervals, of the signalreceived by the second transducer, wherein the successive weighted sumsassociated with successive intervals are themselves formed into aweighted sum;

a measure of the group delay of a portion of the signal received by thesecond transducer; and

a measure of the normalized ratio of narrow-band energy to broad-bandenergy of a portion of the signal received by the second transducer.

In a further embodiment there may be provided a third transducer,affixed to the mounting arrangement, for receiving, along a second paththat is distinct from, and which may be transverse to, the first path,acoustic energy supplied by the first transducer.

In a preferred embodiment, the invention includes one or moretransducers utilizing a piezoelectric crystal element that has an aspectratio that is substantially less than 5:1 and substantially greater than1:5, less than approximately 2:1 and greater than approximately 1:2, andpreferably approximately 1.5:1.

In a further embodiment, the invention provides a system for externallyproviding a measurement in a vertebrate subject of the characteristicbehavior of an acoustic wave in a bone disposed within a body part. Thisembodiment has first and second transducers and a mounting means formounting the transducers in spaced relationship with respect to thebone, all of which are contained in a first assembly. Also provided aresignal excitation means for causing the first transducer to produce anacoustic waveform that is propagated into the subject and received bythe second transducer along a path that includes the bone andcharacteristic determination means for determining a characteristic ofthe behavior of the waveform along the path. A display for displayingoutputs of the characteristic determination means is contained in asecond assembly that is hand-holdable and permits the measurement to betaken while holding the second assembly in one hand of the user. Thesignal excitation means and the characteristic determination means arecollectively contained within the first and second assemblies. Infurther embodiments, the characteristic determination means includes asignal processor for providing a single measurement that is a functionof at least one of spectral or temporal components of a portion, up tothe whole amount thereof, of the signal received by the secondtransducer. The first assembly may be realized as an appliance forremovable engagement with the foot of a subject. The appliance has abase having a surface for receiving the sole of a foot having alongitudinal axis; a cradle rigidly attached to the base, for receivingthe subject's foot and ankle, and disposed in a direction transverse tothe base; a yoke for supporting the transducers in spaced relationshipwith respect to the bone; and a member for mounting the yoke in moveablerelationship to the base so as to permit joint two-dimensional motion ofthe transducers over regions of the heel including the calcaneus. Theyoke and member constitute the mounting means. The member is a backplatehingedly attached at one end to the base along a first hinge axisgenerally transverse to the longitudinal axis; and the other end of thebackplate is hingedly attached, along a second hinge axis generallyparallel to the first hinge axis, to the yoke.

A further embodiment of the invention is the appliance itself, which mayinclude a control module, physically mounted to at least one of thebase, cradle, yoke or member. The module has a first set of data portscoupled to the transducers, a second set of data ports for coupling to(i) a signal excitation means for causing a first one of the transducersto produce an acoustic waveform that is propagated into the subject andreceived by a second one of the transducers along a path that includesthe bone and (ii) characteristic determination means for determining acharacteristic of the behavior of the waveform along the path. Thecontrol module includes a microprocessor for controlling motors forcausing displacement of the yoke and therefore the transducers over thecalcaneus. The module has a control port over which the microprocessorreceives control signals for the motors from a master microprocessor.Preferably, a selected one or both of the transducers employs avibrating element that is sufficiently small as to cause the transducer,if driven by the signal generator, to produce an acoustical output, intothe body part, that is substantially like that of a point source, andeach of the transducers employs a resonating element that has a diameterless than 0.5 cm.

In a related embodiment, the invention provides an apparatus forexternally determining in a vertebrate subject an index of porosity andnon-connectivity of a bone disposed within a body part. The apparatushas first and second transducers; a mounting arrangement for mountingthe transducers in spaced relationship with respect to the bone; asignal generator, in communication with the first transducer, forcausing the first transducer to produce an acoustic signal, havingenergy distributed over a frequency range, that is propagated into thesubject and received by the second transducer along a first path thatincludes the bone; and a signal processor, in communication with thesecond transducer, for providing a single measurement that is a functionof at least one of spectral or temporal components of a portion, up tothe whole amount thereof, of the signal received by the secondtransducer. A selected one or both of the transducers employs avibrating element that is sufficiently small as to cause the selectedtransducer, if driven by the signal generator, to produce an acousticaloutput, into the body part, that is substantially like that of a pointsource; preferably each of the transducers employs a resonating elementthat has a diameter of less than 1 cm.

A further embodiment provides an apparatus for externally determining ina vertebrate subject proximity of an ultrasonic signal path to an edgeof a bone disposed within a body part. The apparatus of this embodimenthas first and second transducers; a mounting arrangement for mountingthe transducers in spaced relationship with respect to the bone; asignal generator, in communication with the first transducer, forcausing the first transducer to produce an acoustic signal, havingenergy distributed over a frequency range, that is propagated into thesubject and received by the second transducer along a first path thatincludes the bone; and a signal processor, in communication with thesecond transducer, for determining a measure of the relative proportionof high frequency energy in relation to low frequency energy of thesignal received by the second transducer. The proportion determined isan indication of the proximity of the first path to an edge of the bone.Preferably, each of the transducers employs a vibrating element that issufficiently small as to cause each transducer, if driven by the signalgenerator, to produce an acoustical output, into the body part, that issubstantially like that of a point source.

In a related embodiment there is provided a method for externallydetermining in a vertebrate subject proximity of an ultrasonic signalpath to an edge of a bone disposed within a body part. The methodincludes providing first and second transducers; mounting thetransducers in spaced relationship with respect to the bone; utilizing asignal generator, in communication with the first transducer, to causethe first transducer to produce an acoustic signal, having energydistributed over a frequency range, that is propagated into the subjectand received by the second transducer along a first path that includesthe bone; and processing the signal received by the second transducer soas to determine a measure of the relative proportion of high frequencyenergy in relation to low frequency energy of the signal received by thesecond transducer. Again, the proportion is an indication of theproximity of the first path to an edge of the bone. Preferably instep(a) each of the transducers employs a vibrating element that issufficiently small as to cause each transducer, if driven by the signalgenerator, to produce an acoustical output, into the body part, that issubstantially like that of a point source.

Another embodiment of the invention provides a method for externallydetermining in a vertebrate subject an index of porosity andnon-connectivity of a bone disposed within a body part. The methodincludes:

(a) providing first and second transducers, wherein a selected one orboth of the transducers employs a vibrating element that is sufficientlysmall as to cause the selected transducer, if driven by the signalgenerator, to produce an acoustical output, into the body part, that issubstantially like that of a point source;

(b) mounting the transducers in spaced relationship with respect to thebone;

(c) utilizing a signal generator, in communication with the firsttransducer, to cause the first transducer to produce an acoustic signal,having energy distributed over a frequency range, that is propagatedinto the subject and received by the second transducer along a firstpath that includes the bone; and

(d) processing the signal received by the second transducer so as toprovide a single measurement that is a function of at least one ofspectral or temporal components of a portion, up to the whole amountthereof, of the signal received by the second transducer.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing features of the present invention will be more readilyunderstood by reference to the following detailed description taken withthe accompanying drawings, in which:

FIG. 1 is a diagram showing in general the components for a system inaccordance with a preferred embodiment of the invention;

FIG. 2 is a diagram showing an implementation of the system of FIG. 1;

FIG. 3A provides a plot showing the stored output of transducer 13 ofFIG. 1 in response to an excitation waveform, generated by the system ofFIG. 1 and transmitted from transducer 12 through water only, as well asplots pertinent to calculation of UBIs in accordance with a preferredembodiment of the invention, shown here as controls;

FIG. 3B provides a plot of the Burg spectral estimation functionassociated with the plots of FIG. 3A;

FIG. 4A provides a plot showing the stored output of transducer 13 FIG.1 in response to an excitation waveform, generated by the system of FIG.1 and transmitted from transducer 12 through a bone having substantialporosity, as well as plots pertinent to calculation of UBIs inaccordance with a preferred embodiment of the invention,

FIG. 4B provides a plot of the Burg spectral estimation functionassociated with the plots of FIG. 4A;

FIG. 5A provides a plot showing the stored output of transducer 13 ofFIG. 1 in response to an excitation waveform, generated by the system ofFIG. 1 and transmitted from transducer 12 through a bone of low-normalquality, as well as plots pertinent to calculation of UBIs in accordancewith a preferred embodiment of the invention;

FIG. 5B provides a plot of the Burg spectral estimation functionassociated with the plots of FIG. 5A;

FIG. 6A provides a plot showing the stored output of transducer 13 FIG.1 in response to an excitation waveform, generated by the system of FIG.1 and transmitted from transducer 12 through an exceptionally healthybone, as well as plots pertinent to calculation of UBIs in accordancewith a preferred embodiment of the invention;

FIG. 6B provides a plot of the Burg spectral estimation functionassociated with the plots of FIG. 6A;

FIG. 7 is a diagram of a preferred embodiment of a hand-heldimplementation shown in FIG. 2;

FIG. 8A is a diagram of a first embodiment of the appliance circuitmodule used in connection with the embodiment of FIG. 7;

FIG. 8B is a diagram of a second embodiment of the appliance circuitmodule used in connection with the embodiment of FIG. 7;

FIG. 9 is a front view of a hand-held device according to the embodimentof FIG. 7;

FIG. 10 is a side perspective view of an appliance in accordance with anembodiment of the invention;

FIG. 11 shows an embodiment of the appliance of FIG. 10, equipped withmagnets and hall effect devices to monitor the location of thetransducers;

FIGS. 12, 13, and 14 provide top, rear, and side views respectively ofthe foot of a subject in relation to a transducer pair T_(T) and T_(R)to illustrate orientation of the transducers in connection with apreferred embodiment of the present invention;

FIG. 15 shows a further embodiment of the invention wherein the subject153 to be tested may occupy a generally horizontal position;

FIG. 16 illustrates in perspective, from a bottom view, an appliancesuitable for use in testing a prone subject;

FIG. 17 is a cross-section of a transducer suitable for use in theappliance of FIGS. 10 and 11; and

FIG. 18 shows detail of the region 178 in an alternative embodiment ofthe transducer of FIG. 17.

FIG. 19 shows the transducer of FIG. 17 surrounded by a sleeve 191.

FIG. 20 illustrates a technique for estimating the instantaneousfrequency of an early portion of the received signal in accordance withthe procedure of UBI-5.

FIGS. 21 and 22 show the narrow-band energy and broad-band energycontent of signals propagated through relatively porous and healthy boneespectively in connection with the procedure of UBI-8.

FIGS. 23 and 24 show the time and frequency domain content of a typicalwaveform received on a path respectively through a central region (shownin FIG. 23) and near the edge (shown in FIG. 24) of healthy calcaneusbone.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS Contents

1. General Arrangements and Signal Generation

2. UBI-2 and Optimized Weighting of Coefficients Generally

3. UBI-3

4. UBI-4

5. UBI-5

6. UBI-6

7. UBI-7

8. UBI-8

9. Composite UBIs

10. Electronics

11. Appliance

1. General Arrangements and Signal Generation

FIG. 1 is a diagram showing in general the components for a system inaccordance with a preferred embodiment of the invention. In this system,a waveform is generated by waveform generator 11, and delivered totransmitting transducer T_(T) , item 12. The transducer T_(T) isacoustically coupled to body part 16 of a subject and produces anacoustic wave that is propagated into the body part 16 and in particularinto a bone within the body part. The transducer T_(R), item 13, is alsoacoustically coupled to the body part 16 and receives a signal resultingfrom the effects, among other things, of propagation of the acousticwave through the bone and the body part. The output of the transducerT_(R) is amplified by amplifier 14 and processed by processor 15. Theprocessor analyzes the output of the transducer T_(R), and may make adetermination reflective of the condition of the bone, and provides anoutput.

FIG. 2 is a diagram showing an implementation of the system of FIG. 1.The body part may be, for example, the region proximate to thecalcaneus. While the elements of FIG. 1 may be implemented in analogcomponents, in a manner known in the art, we have found it convenient touse a digital implementation. Accordingly, the processor 15 and waveformgenerator 11 may be realized in a single hand-holdable unit 27 includinga microprocessor 21 that controls both processing of the output from thetransducer T_(R) and the generation of the waveform used for transducerT_(T). This waveform is stored in digitized form in memory 1, item 24,and under control of the microprocessor is run through digital-to-analogconverter 25 before being provided to amplifier 26 and the transducerT_(T). Similarly, the output of receiving transducer T_(R) is fed fromamplifier 14 to analog-to-digital converter 22 and this digitized outputis stored in memory 2, item 23. The stored output is then processed bythe microprocessor 21, which provides a data output indicating thecondition of the bone.

In further embodiments of the invention, the embodiments of FIG. 2 (or awholly or partially analog implementation of FIG. 1) are used to processthe stored output of T_(R) in accordance with any one or more of avariety of procedures to provide a data output indicating the conditionof the bone. In accordance with some embodiments, the data outputindicating bone condition includes a number, which we call the"Ultrasonic Bone Index" (UBI). Each different procedure we employ canlead to a different UBI, and the various UBI types are identified by anumerical suffix, for example, UBI-2, UBI-3, etc. The procedures forUBI-2 through UBI-8 are described below. In connection with the generalsignal processing techniques utilized (but not their specificutilization in the context of ultrasonic bone testing), the followingreferences are pertinent: Boualem Boashash, ed., Time-Frequency SignalAnalysis (Wiley, 1992)(especially pertinent to instantaneous frequencyanalysis; see especially ch. 2, pages 43-73) and Richard Shiavi,Introduction to Applied Statistical Signal Analysis (Irwin,1991)(especially pertinent to Burg Spectral Estimation; see especiallypages 369-373). These texts are hereby incorporated herein by reference.

Our procedures have been developed to take advantage of the fact thatrelatively nonporous and connective bone, on the one hand, andrelatively porous and non-connective bone, on the other hand, responddifferently to ultrasound inputs. Although it has been known, forexample, that the rate of attenuation with frequency of ultrasoundsignals in bone may be indicative of bone condition, the prior artmeasure of such attenuation, namely broadband ultrasound attenuation(BUA), is based on the assumption that the attenuation is log-linear andprovides a number associated with the rate of log-linear attenuation. Infact, the embodiment of FIG. 2 can be used to calculate BUA. Using thesignal generation arrangement described in the second paragraph below inconnection with the FIG. 2 embodiment the discrete Fourier transform ofthe received signal can be calculated, for example, at five frequenciesfrom 250 kHz to 580 kHz, and these calculations can be the basis fordetermining the BUA. Alternatively, one can compute the Fast FourierTransform of a decimated autocorrelation (with white noise added), andto the resulting spectrum over a broad band, say from 300 kHz to 600kHz, is fitted a straight line, the slope of which is the BUA.

Our investigations have led to the discovery, however, that relativelyconnective and nonporous bone, on the one hand, and relatively porousand non-connective bone, on the other hand, can be better distinguishedby utilizing more information in the ultrasonic signals propagatedthrough bone than is used in arriving at the BUA. We have thus foundthat the difference in effects between strong and porous bone is not onethat can be measured wholly by utilizing the prior art BUA. Theprocedures outlined below take advantage of these and otherobservations.

In the examples that follow, T_(T) is supplied with a short pulse ofabout 500 nanoseconds duration. In this case the pulse has a sawtoothshape, with a rise time to the peak of about 200 nanoseconds and a decaytime of about 300 nanoseconds. The sound output of T_(T) is a shortburst (with some ringing) having a fundamental frequency of about 1 MHz.Because T_(T) is putting out a transient signal, however, usefulcomponents at frequencies within a range from about 200 kHz to 1.5 MHzare present as well. For the purposes of illustration of the nature ofthe burst, FIG. 3A provides a plot 31 showing the stored output oftransducer 13 (T_(R)) of FIG. 1 in response to an excitation waveform,generated by the system of FIG. 1 and transmitted from transducer 12(T_(T)) through water only. (FIG. 3A also shows the Hilbert envelope 32of the waveform 31, while FIG. 3B shows the Burg spectral estimationfunction associated with the waveform 31. These concepts are discussedbelow.) Also as described in further detail below, the transducers arein this embodiment designed to generate a small-sized excitation area(of the order of 0.3 cm) and to have substantially non-directionalcharacteristics, so that the transmitting transducer 12 behavessubstantially like a point source. And the receiving transducer behavessubstantially like a point receiver.

The received signal is, of course, influenced not only by the excitationarea of the transmitting transducer 12 and the size of the receiver butalso by the signal path. Given the physical size of the calcaneus andthe speed of ultrasound in bone, it takes approximately 30 μsec afterinitiation of the burst for any output to be received by the receivingtransducer 13. For example, a duration window of 10 μsec after this 30μsec delay permits analysis of signal due to all signal paths having alength between 4.5 cm and 6.0 cm, assuming a velocity of 1500 m/sec.Analysis of received signal behavior that occurs approximately withinthis window is advantageously used in accordance with a preferredembodiment of the invention, although other windows are within the scopeof the present invention.

2. UBI-2 and Optimized Weighting of Coefficients Generally

In accordance with UBI-2, the stored output of T_(R) is run through adiscrete Fourier transform. A weighted linear sum of the logarithm ofresulting frequency components is then computed; this sum is UBI-2. Theweights are chosen to minimize differences among successive measurementstaken of the same individual and to maximize differences in measurementstaken of different individuals, so that the function acts as adiscriminant in determining the extent of non-connectivity and porosityof bone. The weights may be selected empirically using manualtechniques. They may also be selected using neural net techniques knownin the art; see U.S. Pat. No. 5,259,384 for an invention of Kaufman.They also may be determined analytically in accordance with the methoddescribed below in the next two paragraphs.

An analytic method for optimization of linear coefficients method isdescribed in this paragraph. Suppose that repeated observations are madeon individuals in a population. Thus, in each experiment we measure avector v=(v₁, . . . ,v_(n)). (This vector v may, for example, constitutethe magnitudes of n frequency components of the received signal; but itmay be any other set of measurements associated with an individual, asdiscussed in further detail below.) We seek the coefficients a_(k) of alinear combination of these vector components v_(k), thus: ##EQU1## insuch a way that the "score" s minimizes the variance attributable torepeated measurements taken of the same individual while at the sametime maximizing the range of the score and approximately conforming toour prior notions of how the individual should score. Thus a_(k) is a"weight" assigned to the k-th variable v_(k) of the vector v, and we aresearching for an optimal weighted linear combination of the variables.In order to specify the method for doing this, we assume that therepeated measurements have been made that lead to vectors v(i,j), whichare the results of the j-th measurement on individual i. A weightingvector a=(a_(k))(k=1, . . . , n) leads to a score of the form ##EQU2##

The mean score on individual i is S_(a) (v(i)), where ##EQU3## is themean of the observations on individual i and N_(i) observations are madeon individual i. The average "within-individual" variance, where thereare N individuals, is therefore ##EQU4##

Now let ##EQU5## be the average of the observations of all individuals.Then the "between-individuals" population variance is ##EQU6##

We want to find a scoring vector such that the quotient ##EQU7## isminimized. This "generalized Rayleigh quotient" is a quotient ofquadratic forms, and is optimized by choosing a minimal generalizedeigenvalue λ

where

    Aa=λBa

and where the matrices A and B correspond to the quadratic forms in theusual way:

    I(a)=a.sup.tr A a,P(a)=a.sup.trB a.

The calculation of these generalized eigenvalues can be performed inseveral ways well known in the art. See for example, J. Stoer and R.Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, New York,Second Edition, 1991), page 405, which discusses generalized eigenvalueproblems. The upshot is that the coefficients of an optimal linear modelbuilt on the data v can be obtained by combining the observed data intothe above linear model.

It is possible to incorporate prior subjective scores into thisprocedure. More precisely, suppose that we believe that individual ishould have the score s_(i). Then we modify the above problem byreplacing I(a) by ##EQU8## where t is a parameter that determines howheavily we want to force the computed scores to match our prior beliefs.The resulting problem is identical in form to the prior one, except thatthere are two new variables a_(n+1) and a_(n+2). If the parameter t islarge then this becomes a linear regression problem. If the parameter issmall, then we are more interested in minimizing the average variance(as a fraction of the population variance) as above. The method assumesthat the scores should depend only linearly on the measured values. Wefind that experimentation is valuable, both for choosing whichobservations to consider, and for choosing the parameter t.

It will be appreciated that the weights determined using any of theprocedures above are dependent on the precise characteristics of thesystem employed, including characteristics of the transducers, thewaveform input to T_(T), the circuits and processing associated with thesignal from T_(R), and the data with respect to which the weights areoptimized. A sample set of weights for UBI-2 is set forth in Table 1below.

                  TABLE 1                                                         ______________________________________                                        Frequency                                                                              Program      Simplified                                                                             Constrained                                    (MHz)    Weights      Weights  Weights                                        ______________________________________                                        0.000    0.0718       0.0      0.0                                            0.125    1.0000       1.0      1.0                                            0.250    0.225        0.2      0.0                                            0.375    -0.406       -0.4     -0.4                                           0.500    -0.0767      0.0      0.0                                            0.625    -0.506       -0.5     -0.6                                           0.750    -0.0372      0.0      0.0                                            0.875    -0.139       -0.1     0.0                                            1.000    -0.0365      0.0      0.0                                            1.125    -0.0486      0.0      0.0                                            1.250    0.0946       0.0      0.0                                            1.375    -0.00858     0.0      0.0                                            ______________________________________                                    

The data in Table 1 were derived from data collected on 21 subjects. Theweights for each frequency component used in UBI-2 appear in columns 2,3, and 4. In the second column are weights as calculated using theanalytical approach discussed above. In the third column are the weightsresulting after using only the five largest weights and then rounding toone significant figure. This column produces results that are onlyslightly degraded from those using the weights in column 2. In column 4are weights resulting after using only the three largest weights andthen modifying them slightly so that they sum to 0. The column producesresults that in turn are only slightly degraded from those using theweights in column 3. It is preferred to use weights in this context thatsum to 0, so that a change in gain does not produce a change in theresulting UBI-2. Note that the weights in Table 1 are greatest in theregions of 100-200 kHz (positive) and 500-700 kHz (negative).

3. UBI-3

The UBI-3 procedure utilizes the Hilbert envelope of the stored outputof T_(R) ; the Hilbert envelope provides a measure of the energy contentof the received waveform as a function of time. The greaterpreponderance of low frequency signals in the received waveformassociated with healthy bone causes it to have a longer duration than inthe received waveform associated with relatively porous bone.Accordingly, in accordance with UBI-3, the Hilbert envelope is examinedfor energy duration. A relevant time period of the stored output isexamined; for this time period, there is determined the fraction of arealying above the plot (of the top half of the envelope) and beneath afixed value defined by the first peak in the plot. In one embodiment,the relevant period begins 1 microsecond after the first peak in theHilbert envelope and continues for a total of 8 microseconds. In afurther embodiment, UBI-3 is instead the curvature of the envelope overthe first few microseconds following the first peak.

FIGS. 3A, 4A, 5A, and 6A are illustrative for the case of transmissionthrough water, relatively porous bone, low-normal bone, andexceptionally healthy bone respectively. Plots 31, 41, 51, and 61 showthe stored output of transducer T_(R) for such respective circumstances,and plots 32, 42, 52, and 62 show the corresponding Hilbert envelopes.It can be seen that hatched region 45, corresponding to the UBI-3 for arelatively porous bone, is much larger than hatched region 55,corresponding to the UBI-3 for a low-normal bone.

4. UBI-4

The UBI-4 procedure utilizes an autoregressive moving average (ARMA)spectral estimation function of the stored output of T_(R). In oneembodiment, UBI-4 uses the Burg spectral estimation function of thestored output of T_(R) ; the Burg function provides a plot estimatingpower versus frequency of the received waveform. The shape of the plotis a discriminant between healthy and relatively porous bone. UBI-4 isan estimate of the slope; generally the more steeply negative the slope,the healthier the bone. In this connection, see plots 34, 44, 54, and 64in FIGS. 3B, 4B, 5B, and 6B respectively for the case of transmissionrespectively through water, relatively porous bone, low-normal bone, andexceptionally healthy bone. In one embodiment, the UBI-4 slope of theplot is determined by best fit to the plot using mean square error. Inanother embodiment, the slope is determined in reference to the averagesover two adjacent frequency regions, each of 200 kHz in width; the firstfrequency region starts at the first peak in the plot and the secondfrequency region starts 200 kHz higher. As an example, see areas 56 and57 respectively in FIG. 5B, corresponding to the first and secondregions. The proportional difference in these averages is indicative ofthe slope, which is shown as line 58 in FIG. 5B. In a furtherembodiment, the slope is determined by reference solely to two points onthe plot, the first occurring at the first peak, and the secondoccurring 400 kHz higher in frequency. As an example, see line 59 inFIG. 5B.

5. UBI-5

The UBI-5 procedure estimates the instantaneous frequency during theearly portion of the received waveform. One embodiment utilizes theHilbert frequency function. This function is plotted as item 43 and 63in FIGS. 4A and 6A respectively for relatively porous bone andexceptionally healthy bone respectively. It can be seen that for healthybone, during the early portion (3 or 4 microseconds) of the receivedwaveform, there is little variability, whereas for relatively porousbone, there is considerable variability including higher frequenciesthan for healthy bone. The variability can be quantified according toany of a variety of methods well-known in the art.

As an alternative, or in addition, to measuring the variability of theHilbert frequency function with time, it is possible to determine themean frequency of the first half-cycle of the received burst. (As isknown in the art of signal processing, ordinary Fourier analysis cannotbe used for, and is inapplicable to, such a short sample.) A comparisonof the mean frequency indicated by curve 43 of FIG. 4A during the firsthalf cycle of received signal and the mean frequency indicated by curve63 of FIG. 6A during the first half cycle of received signal shows thatthe bad bone has a dramatically higher mean frequency during thishalf-cycle. One way of making this frequency determination is to laborthrough calculation of the Hilbert function over the course of thishalf-cycle and then determine its average over the interval.

Alternatively, we have found that the average first half-cycle frequencycan be estimated with good success. FIG. 20 illustrates a technique forestimating the instantaneous frequency of an early portion of thereceived signal in accordance with UBI-5. As shown in FIG. 20, merelyusing the zero crossings 202 and 203 of the received signal 201 producesa half-period T₀ that is too long (and a resulting frequency that is toolow) to match the frequency most closely associated with the first halfcycle. In other words, a sine wave having the half-period T₀ would betoo broad to coincide with the first peak 208 of the received signal. Wehave found that a more accurate estimate of average frequency can beobtained by first identifying the points 204 and 205 on either side ofthe peak where the slope of the curve changes between increasing anddecreasing (that is, where the second derivative with respect to time iszero). Next, the intercepts 206 and 207 of tangents to the signal curveat points 204 and 205 are determined. The duration between theseintercepts 206 and 207 is the half-period T₁, which is used to determinethe first half-cycle average frequency.

An alternative method of estimating the average first half-cyclefrequency is to is to find the frequency that produces a least meansquare error fit of a sine wave to a small zone surrounding an earlypeak 208.

6. UBI-6

The UBI-6 procedure utilizes the short-time Fourier transform of thestored output of T_(R) to examine in more detail than with the Hilberttransform the varying spectral content of the received waveform overtime. A frequency index may be computed in a fashion analogous UBI-2 orUBI-4. The temporal variation of this index may be used to compute adifferent index in a fashion analogous to UBI-5.

7. UBI-7

The UBI-7 procedure utilizes the Fourier transform of the stored outputof T_(R) to produce data permitting a plot of phase versus frequency;the slope of this plot is a measure of velocity (as a function offrequency). The variation of velocity with frequency (i.e., group delay)is dispersion, which can be quantified according to any of a variety ofmethods. In the relatively porous bone, there is relatively littledispersion; in relatively nonporous bone, there is relatively moredispersion.

8. UBI-8

The UBI-8 procedure is premised on the recognition that bad boneproduces a broad band signature, whereas good bone tends to passrelatively low frequencies more selectively. Accordingly, UBI-8 involvesthe determination of (i) "narrow-band energy," which, for the purposesof this description and the following claims, is the energy associatedwith 100 kHz of spectrum surrounding the low-frequency spectral peak,and (ii) "broad-band energy," which, for the purposes of thisdescription and the following claims, is the energy associated with thefull spectrum of 0-1000 kHz. UBI-8 is the normalized ratio ofnarrow-band energy to broad-band energy.

FIGS. 21 and 22 show the narrow-band energy and broad-band energycontent of signals propagated through relatively porous and healthy bonerespectively in connection with the UBI-8 procedure. The narrow-bandaverages for relatively porous and healthy bone are shown as linesegments 211 and 221 respectively, and the associated narrow-band energycontent in each case is the area under each of these segments. Similarlythe wide-band averages for relatively porous and healthy bone are shownas line segments 212 and 222 respectively, and the associated wide-bandenergy content in each case is the area under each of these segments.Thus in the case of relatively porous bone in FIG. 21, the narrow-bandenergy content is about 10% of the wide-band energy content. Incontrast, in the case of healthy bone in FIG. 22, the narrow-band energycontent is much greater than 10% of the wide-band energy content.

9. Composite UBIs

Although any one of the UBIs discussed may be used alone, it is alsopossible to use combinations of any number of them to enhancesensitivity and specificity in identifying relatively porous bone.Indeed a single composite UBI may be derived as a function (which neednot be linear) of the UBIs described above. The function may be theweighted sum, and the weights may be determined in the manner describedabove in connection with UBI-2: empirically, or using neural networks,or using the closed form analytical procedure described above.

In one embodiment, we have found it useful to take a UBI of the typedescribed above and divide it by an estimate of heel width. The estimatecan be derived from a determination of the delay between initiation ofthe burst in transducer T_(T) and the arrival of the burst in the signalreceived by T_(R). This quotient is therefore roughly normalized to takeinto account heel width.

10. Electronics

The procedures described above may be employed in a device such as shownin FIG. 7, which is a diagram of a preferred embodiment of theimplementation shown in FIG. 2. The device operates under the control ofmicroprocessor 72, which is here implemented as a Motorola 68HC341. Themicroprocessor communicates with a data bus 729 and an address bus 720.In communication with these buses are static RAM 724 (here implementedas 32K times 16, to accommodate a 16-bit word), flash RAM 725 (hereimplemented as 2048K times 16), and PCMCIA slot 726 for communicationvia modem and potentially for other purposes. The device is alsoprovided with first and second serial ports 731 and 732 respectively,coupled to the microprocessor 72 via dual RS-232 transceiver 73, fordata input and output, permitting attachment of an external modem anddirect communication with a PC. User input to the device is achievedlocally via keypad 75, coupled to register 727, which is on the data bus729. The device has a video output on display 76, here an LCD bit-mappeddisplay having a resolution of 64×128 pixels, that is in communicationwith register 728 and data bus 720. The excitation waveform to drive thetransducer T_(T) of FIG. 2 is stored in Flash RAM 725 and is loaded intostatic RAM 724 over data bus 729; the static RAM transfers the waveformby direct memory access (DMA) into digital-to-analog converter 723,which provides an output over line 912 to appliance connector 71 todrive the transducer T_(T). The waveform output from transducer T_(R) ofFIG. 2 is communicated to line 711 of connector 71, and then throughvariable gain amplifier 721 to analog-to-digital converter 722. The gainof amplifier 721 is adjusted by the microprocessor 72 over gain selectlines. The output of the converter 722 is communicated over data bus 729to static RAM 724, where the received waveform data is captured. Thedata can then be processed by microprocessor 72 (according to theprocedures described above), and UBI and other data can be presented tothe user, both via the display 76 and over the ports 731, 732, and thePCMCIA slot 726. The transducers are here driven by a separate appliancemodule, described below in connection with FIGS. 8A and 8B, to whichconnection is made through appliance connector 71. The module iscontrolled by a dedicated microprocessor communication with which isover control line 713. Power is provided by power supply 77, which iscoupled to battery 771 and battery charger 792, which in turn isconnected to power jack 773.

In addition, we have found it valuable to provide a speaker 741 (audiojack 742 is also provided) coupled via audio amplifier 74 todigital-to-analog converter 723 to permit "listening" to the storedwaveform received from transducer T_(R). The listening is made possibleby playing back the stored signal at 1/1000 th of the original frequencyand over an extended duration. The trained ear can distinguish manyfeatures of the waveform in this manner. The speaker can be used,moreover, similarly to listen to the waveform processed in otherrespects as well--processed, for example, in accordance with one or moreof the UBI procedures described above. It can also be used to provideaudible cues to the user, for example in positioning the appliance, sothat a continuous analog signal indicative of position can guide theuser, who will not then need to watch the display 76 while positioningthe appliance.

FIG. 8A is a diagram of a first embodiment of the appliance circuitmodule used in connection with the embodiment of FIG. 7. The applianceconnector 81 of FIG. 8 mates with connector 71 of FIG. 7. Control line713 of FIG. 7 is connected through the connectors to control line 813 ofFIG. 8, so that control signals run between slave microprocessor 84(implemented here as Motorola 68HC711E9) and main microprocessor 72 ofFIG. 7. The excitation line 712 of FIG. 7 is connected through theconnectors to line 812 of FIG. 8 and driver amplifier 822, which ispowered by a 300 volt supply. The received waveform line 711 of FIG. 7is connected through the connectors to line 811 of FIG. 8A whichreceives an output from variable gain amplifier 821. The output ofamplifier 822 and the input of amplifier 821 are connected to a relaymatrix 83 that is driven by relay drivers 842 under control ofmicroprocessor 84.

The relay matrix 83 permits the input of amplifier 821 to be connectedto any of a series of, say, three transducers and the output ofamplifier 822 to be connected to any other of the series of transducers.This arrangement has the advantage that the specific transducers usedfor transducers T_(T) and T_(R) may be switched, as desired, to assuresymmetry of the system in either configuration and/or to compensate forthe lack of symmetry. It also permits the use of a third transducer fora variety of purposes, including those described in U.S. Pat. No.5,396,891, wherein three transducers are used in velocity measurements.

We have also found that when two transducers (producing preferably inthis case a columnated beam) are used for ultrasound signaltransmission, a substantial portion of the waveform energy nottransmitted directly through the calcaneus can be detected bypositioning a third transducer in a position distinct from the secondtransducer around the periphery of the heel to receive scattered orbackscattered acoustic radiation. The signal from this third transducercan provide information complementary to, or overlapping, that obtainedwith the initial two transducers associated with direct transmission.

The microprocessor 84 also communicates optionally with motor decoder85, which is coupled to drivers 851, 852, and 853 for motors 1, 2, and 3respectively. These motors control the position of the transducersrelative to the body part including the bone under measurement. Themotors may be usefully used to assure correct positioning of thetransducers for the measurements being made. Indeed, it appears thatrelative porosity may appear preferentially not only in certain bones ofa subject but also in one or more regions of such certain bone, such asthe calcaneus. In accordance with an embodiment of the presentinvention, one or more of the transducers T_(T) and T_(R) --and (in afurther embodiment) both such transducers--are moved, over a pertinentregion of the bone, either by the user or under microprocessor control,until an optimized reading (determined by one or more of the aboveprocedures or otherwise) has been obtained, and then the measurements inthe position associated with this optimized reading in accordance withthe above procedures are completed and stored.

FIG. 8B is a diagram of a second embodiment of the appliance circuitmodule used in connection with the embodiment of FIG. 7. In thisembodiment, the motor drive circuits have been eliminated, only twotransducers are employed, and these transducers, T_(T) and T_(R), aremoved manually utilizing the appliance described below in connectionwith (for example) FIG. 10. Additionally, there are provided a pair ofHall effect sensors 801 and 802 to sense position (as described inconnection with FIG. 11) of the transducers and a temperature sensor 803to enable temperature compensation; the outputs of these transducers areamplified by amplifiers 806, 805, and 807 respectively, converted todigital format by an A-to-D converter associated with microprocessor 84,and then used as processing inputs. Gain for amplification of the signalreceived by transducer T_(R) is adjusted by themicroprocessor-controlled switch 825, which in a first position isconnected to the output of first amplifier 823, and in a second positionis connected to the output of second amplifier 824, which as its inputthe output of amplifier 823.

FIG. 9 is a front view of a hand-held device 90 according to theembodiment of FIG. 7. All of the circuitry of the device of FIG. 7 iscontained in a single unit, permitting excitation of the appliancetransmitting transducer and processing of waveform data from theappliance receiving transducer(s) and storage and display of theresults. The device has a housing 91, in which is provided the display92 (item 76 of FIG. 7) and keypad 93 (item 75 of FIG. 7). The devicealso has the ports and other features described above in connection withFIG. 7.

11. Appliance

FIG. 10 is a side perspective view of an appliance in accordance with anembodiment of the invention. The appliance includes a base 101 to whichis attached rigidly a cradle 102 for the subject's foot and ankle. Thesubject's heel (and, if desired, neighboring regions) may be bare, or itmay be placed, for purposes of hygiene, in a glove-like covering. Toassure good ultrasound conduction, the covering is preferably thin,tight-fitting, and elastic. Alternatively, or in addition, the coveringmay be coated on the inside with a suitable material, such as awater-based gel, to assist in ultrasound conduction. (The effects ofthese materials may be compensated in signal processing of the receivedwaveform.) The region of the cradle 102 corresponding to the calcaneusincludes a cutout 106 on each side to accommodate a receiving transduceron one side and a transmitting transducer on the other side. Thetransducers are mounted in generally opposed relation to one another (inlocation 104 for the lateral transducer) in a yoke 103 that is movablymounted relative to the base 101 and cradle 102. In this embodiment theyoke 103 has two degrees of freedom, achieved by mounting the yoke 103via a hinge at axis Y--Y to backplate 105, and mounting the backplate105 via a hinge at axis X--X to the base 101. The appliance module ofFIG. 8B is here physically mounted inside the backplate 105. Cable 107with connectors 108 and 109 permits communication respectively betweenthe appliance module and the hand held device 90 described in connectionwith FIG. 9 and provides power to the appliance module from the device90.

The position of the transducers may be monitored by usingpotentiometers, shaft encoders, or other suitable sensors disposed inrelation to the axes X--X and Y--Y. In addition, the sensors arepreferably biased inwardly toward each other (by one or more springs orother means) to assure good contact with the heel area of the subjectfor ultrasound transmission. If desired, the distance between thetransducers can be determined indirectly, by mounting each transducer ona separate arm that is pivotally mounted at one end to the yoke, and theangle that the arm makes at the pivot can be monitored by suitablesensors; the arm angles, in combination with a knowledge of the geometryof the yoke assembly, can be used to calculated the distance between thetransducers. Such distance information is useful for ultrasound velocitydeterminations and for normalization of UBI values.

Positioning of the transducers in relation to the axes X--X and Y--Y isimportant to assure that the transducers are located away from edges ofthe calcaneus. We have found that positioning the transducers near anedge of the calcaneus has a profound effect on the received waveform.Furthermore, we have found that appropriate signal processing of thereceived waveform permits one to detect proximity to an edge of thecalcaneus, so that the transducers may be located in a position, awayfrom the edge, that results in signal transmission and reception througha central region of the calcaneus.

For detection of an edge of the calcaneus it is possible to utilize oneor more UBI values determined in the manner described above. Forexample, when the ultrasound path is near the edge of a bone orpredominantly in soft tissue, the various UBI values will result in anindex identifying relatively porous and non-connective bone.Alternatively, we have found that quantifying the relative amount ofenergy in the received waveform at high frequencies in relation to thatat low frequencies produces a test that is particularly sensitive tobone edges. This phenomenon is illustrated in FIGS. 23 and 24. In FIGS.23 and 24 are shown the time and frequency domain content of a typicalwaveform (as discussed in connection with the embodiments above)received on a path respectively through a central region (shown in FIG.23) and near the edge (shown in FIG. 24) of healthy calcaneus bone. Itcan be seen in FIG. 23 that the energy in the received waveform on acentral path is concentrated below about 800 KHz, whereas the energy inthe received waveform on the edge path (in FIG. 24) is rich in highfrequencies. The relative absence of high frequencies associated withpositioning of the signal path away from the edge can be quantified invarious ways. One usable test is to compute the fraction of highfrequency energy (defined here and in the claims as energy atfrequencies between approximately 900 KHz and approximately 1.2 MHz) inrelation to the low frequency energy (defined here and in the claims asenergy at frequencies between approximately 300 and approximately 600KHz) in the received signal. In the case of FIG. 23, the fraction isless than 1%, whereas in FIG. 24 the fraction is over 100%. This testcan be used to determine appropriate positioning of the signal path (bymotion of the yoke 103 of FIG. 10). The test may be conducted in realtime to determine appropriate positioning, or alternatively, since thereceived signal can be sampled and stored, one may record the waveformsfor a variety of transducer positions, and thereafter select therecorded waveform or waveforms that indicate appropriate positioning;the selected waveform or waveforms can then furnish the basis for theUBI determination as described above.

FIG. 11 shows an embodiment of the appliance of FIG. 10, equipped withmagnets and Hall effect devices to monitor the location of thetransducers, mounted in the yoke 103, in holders 111. In this embodimenta first ceramic magnet 112 is mounted on the base 101 and a secondceramic magnet 113 is mounted on the yoke 103. Hall effect magneticsensors 114 and 115 are mounted on stalks on backplate 105 in to detectthe magnetic fields of magnets 112 and 113 respectively. The signalstrengths of the outputs from Hall effect sensors 114 and 115 aretherefore indicative of the degree of rotation respectively of backplate105 about axis X--X and of yoke 103 about axis Y--Y. These outputs arelinearized with angle by geometrically aligning each magnet and sensorpair so as to combine the 1/r effect (at these distances) ofmagnet-sensor distance and the sine θ effect of sensor angle in themagnetic field. Accordingly, the outputs of Hall effect sensors can bemapped, under microprocessor control, into suitable rectangularcoordinates to identify the location of the transducers in relation tothe subject's heel.

As discussed above in connection with FIGS. 8A and 8B, the yoke may bemoved manually or it may be moved under motor control by suitablymounted motors associated with each degree of freedom.

FIGS. 12, 13, and 14 provide top, rear, and side views respectively ofthe foot of a subject in relation to a transducer pair T_(T) and T_(R)to illustrate orientation of the transducers in connection with apreferred embodiment of the present invention. Here the separatetransducers T_(T) and T_(R) are here generically identified as T_(a)regardless of function. Because the transducers act approximately aspoint sources and point receivers--unlike transducers used in prior artdevices--they need not be placed in coaxial alignment. Indeed, it isdesirable that they be oriented so as to be approximately normal to thesurface of the heel at the point of contact with the heel. The effect ofplacement in this orientation is that the axes of the transducers arenot coaxial; the axes are skewed with respect to one another in twodistinct planes, the horizontal and the vertical. In FIG. 12 the linethrough the two points of contact of the transducers with the heel isshown as A--A. The central longitudinal axis of each transducer is shownas P. It can be seen that each transducer axis P is oriented in arearward direction with respect to the points of contact axis A--A by anangle θ, which in practice is about 20 degrees. Similarly, shown in FIG.13 is a rear view of the foot of a subject including the medialmalleolus 131 and lateral malleolus 132. In this view it can be seenthat each transducer axis P is oriented in an upward direction withrespect to the points of contact axis A--A by an angle φ, which inpractice is about 10 degrees. As shown in connection with the side viewin FIG. 14, the effect of this orientation is each transducer pointsboth down and forward in order to be approximately normal to the heel atthe point of contact. This orientation can be achieved by appropriateconfiguration of the yoke 103 and related components in FIGS. 10 and 11.

While an advantage of the appliance illustrated in FIGS. 10 and 11 isthat the subject may be tested when the subject is either standing orseated with feet on the floor, there is an attendant disadvantage inthat the subject's foot is difficult to immobilize in the appliance whenthe subject is in such a position. In a further embodiment of theinvention, shown in FIG. 15, the subject 153 to be tested may occupy agenerally horizontal position on a conventional physician's examinationtable 151 or other horizontal surface. The appliance 152 may thus befitted onto the subject 153 when the subject is lying on the back. Whenthe subject's foot is extended after the appliance 152 is fitted ontothe subject, the foot is supported both by the appliance 152 and by theexamination table 151 and is less prone to movement within the appliance152.

In FIG. 16 is illustrated in perspective, from a bottom view, anappliance suitable for use in testing a prone subject. The appliance isconfigured and used in the general manner of the appliance of FIGS. 10and 11. The appliance here has a base 162 to which is rigidly attached acradle 166 for the subject's foot and ankle. In this embodiment,however, the base 162 is itself rigidly mounted to horizontal support163, which typically rests on the examination table 151 of FIG. 15.Strap 167 may be used to removably secure the subject's foot in thecradle 166. The cradle 166 includes a cutout on each side in the regioncorresponding to the calcaneus to accommodate the transducers T_(T) andT_(R), which are mounted to yoke 161 on opposite sides of the calcaneus;the yoke 161 is movably mounted with respect to base 162 and support163. As in the case of the appliance of FIGS. 10 and 11, the traducersmay be moved manually or by motors under control of a microprocessor.Case 168 may be used to hold the appliance module of FIG. 8A or 8B.Alternatively, case 168 may house the equivalent of both the appliancemodule and the device of FIG. 7. In the latter case, the case 168 may befitted with display 169, a keyboard, etc. It is also within the scope ofthe present invention to have the appliance operate in wirelesscommunication (using rf or infra red) with a base unit that may but neednot be hand held or hand-holdable, and in such an instance, the display169 can be used to indicate the presence of satisfactory orientation ofthe appliance and the transducers or to provide other pertinentinformation to the operator.

FIG. 17 is a cross-section of a transducer suitable for use in theappliance of FIG. 10. The traducer utilizes a piezoelectric crystalelement 173, which is unusual in that its aspect ratio is of the order1.5:1. (As used in this description and the following claims, "aspectratio" is the ratio of diameter to thickness.) Such a ratio is usuallyviewed as undesirable, and more typical aspect ratios are at least 5 or10:1, so as to avoid undesirable resonances in directions other than thetransverse plane from which the ultrasound is to be propagated. In thepresent case, however, we have found that our design adequately controlsmultiple resonances and yields desirable near point-source behavior andwide bandwidth. Typical dimensions for a piezoelectric element of ourdesign are a diameter of 0.125 inches (0.32 cm) and a thickness of 0.080inches (0.20 cm). The element rests between metal base 172 and frontface element 174, which are connected to the center and outsideconductors respectively of a suitable coaxial cable 171. The front face174 plays a role in the frequency response of the transducer, and itsthickness is chosen empirically to optimize the frequency response. Inpractice, it has been found desirable to construct the front face 174 ofepoxy with a thickness of 0.025 inches (0.6 mm). The transducer isdisposed in a housing 176; the housing serves as both a mechanicalanchor for the transducer and as an electrical shield, and is preferablyof a metal, such as, for example, brass. The base 172 is placed withinacoustically absorbent backing 175 to damp ringing, and the back end ofthe assembly is held in place with epoxy 177.

FIG. 19 shows the transducer of FIG. 17 surrounded by a sleeve 191. Inmounting the transducer 17 of FIG. 17 in the yoke 103 of FIG. 10, wehave found it beneficial to surround the case 176 with a sleeve 191 of asuitable material such as Delrin plastic. The collar serves not only toreceive spring pressure for spring-loading against the body but also todeflect ultrasound in a desired direction. The sleeve 191 may be sealedagainst the case of the transducer with a material such as siliconrubber. Alternatively, the sleeve may be made of metal and integrallyformed with the case 176. A typical thickness of the sleeve wall isapproximately 1/4 inch (6 mm). As shown in FIG. 19, the end of thesleeve providing an opening to the transducer has an outside perimeter192 that is preferably rounded.

FIG. 18 shows detail of the region 178 in an alternative embodiment ofthe transducer of FIG. 17. In FIG. 18, the absorbent backing 175 isextended into the area around the perimeter of the piezoelectric element173 that is adjacent to and in front of it. The effect of thisadditional backing material is reduce the extent of epoxy around theperimeter of the face to better direct ultrasound energy toward thesubject.

The transducer of FIG. 17 produces an excitation area that is about anorder of magnitude smaller than the 3 cm beam produced by typicaltransducers used in prior art devices for measuring bone soundness.Moreover, in the preferred embodiments of the present invention, thetransducer is engaged proximately to the calcaneus, whereas in manyprior art devices, the transducer is spaced in the vicinity of 5 cm ormore from the surface of the heel. Given the relatively smallarea--about 5 cm in diameter--of the target calcaneus bone, the largebeam signature of the prior art transducers is subject to greatercontamination by the effects of the bone boundary. Use of the transducerof FIG. 17 as the transmitter approximates the behavior of a pointsource, and use of a similar transducer as the receiver approximates thebehavior of a point receiver, so that effects of the bone boundary maybe minimized. Furthermore, the transducer of this design radiates andreceives effectively over a wide angular range, permitting optimizationof direct coupling to the body part based on anatomical features ratherthan on the need to maintain coaxial orientation as in the case of priorart transducers.

What is claimed is:
 1. An apparatus for externally determining in avertebrate subject an index of porosity and non-connectivity of a bonedisposed within a body part, the apparatus comprising:(a) first andsecond transducers; (b) a mounting arrangement for mounting thetransducers in spaced relationship with respect to the bone; (c) asignal generator, in communication with the first transducer, forcausing the first transducer to produce an acoustic signal, havingenergy distributed over a frequency range, that is propagated into thesubject and received by the second transducer along a first path thatincludes the bone; and (d) a signal processor, in communication with thesecond transducer, for providing a single measurement that is a functionof at least one of transient spectral or transient temporal componentsof a portion, up to the whole amount thereof, of the acoustic signalreceived by the second transducer, so that the measurement relates tothe extent of non-connectivity and porosity of the bone.
 2. An apparatusaccording to claim 1, wherein the function is a weighted sum of aplurality of other functions of at least one of transient spectral andtransient temporal components of a portion, up to the whole amountthereof, of the signal received by the second transducer, and theweights are selected for their ability to minimize the differences amongsuccessive measurements taken of the same individual and to maximizedifferences in measurements taken of different individuals.
 3. Anapparatus according to claim 2, wherein the weighted sum is of spectralcomponents of the signal received by the second transducer.
 4. Anapparatus for externally measuring in a vertebrate subject an index ofporosity and non-connectivity of a bone disposed within a body part, theapparatus comprising:(a) first and second transducers; (b) a mountingarrangement for mounting the transducers in spaced relationship withrespect to the bone; (c) a signal generator, in communication with thefirst transducer, for causing the first transducer to produce anacoustic signal, having energy distributed over a frequency range, thatis propagated into the subject and received by the second transduceralong a first path that includes the bone; and (d) a signal processor,in communication with the second transducer, for providing a singlemeasurement that is a function of at least one of spectral or temporalcomponents of a portion, up to the whole amount thereof, of the acousticsignal received by the second transducer, such measurement being otherthan a function based solely on Fourier spectral information.
 5. Anapparatus according to claim 4, wherein the function includes a weightedsum of spectral components of a portion of the signal received by thesecond transducer.
 6. An apparatus according to claim 4, wherein thefunction includes a measure of the shape of the Hilbert envelope of aportion of the signal received by the second transducer.
 7. An apparatusaccording to claim 4, wherein the function includes a measure of theshape of an autoregressive moving average spectral estimation functionof a portion of the signal received by the second transducer.
 8. Anapparatus according to claim 4, wherein the function includes a measureof the variability of the Hilbert frequency function of a portion of thesignal received by the second transducer.
 9. An apparatus according toclaim 4, wherein the function includes a measure of the average Hilbertfrequency function of an early portion of the signal received by thesecond transducer.
 10. An apparatus according to claim 4, wherein thefunction includes a weighted sum of spectral components, determinedusing a short-time Fourier transform, and determined at successiveintervals, of the signal received by the second transducer, wherein thesuccessive weighted sums associated with successive intervals arethemselves formed into a weighted sum.
 11. An apparatus according toclaim 4, wherein the function includes a measure of the group delay of aportion of the signal received by the second transducer.
 12. Anapparatus according to claim 4, wherein the function includes a measureof the normalized ratio of narrow-band energy to broad-band energy of aportion of the signal received by the second transducer.
 13. Anapparatus according to claim 4, further comprising:a third transducer,affixed to the mounting arrangement, for receiving, along a second paththat is distinct from the first path, acoustic energy supplied by thefirst transducer.
 14. An apparatus according to claim 13, wherein thesecond path is transverse to the first path.
 15. An apparatus accordingto claim 4, wherein a selected one of transducers includes apiezoelectric crystal element that has an aspect ratio that issubstantially less than 5:1 and substantially greater than 1:5.
 16. Anapparatus according to claim 4, wherein a selected one of transducersincludes a piezoelectric crystal element that has an aspect ratio thatis less than approximately 2:1 and greater than approximately 1:2. 17.An apparatus according to claim 15, wherein the aspect ratio isapproximately 1.5:1.
 18. An apparatus for externally measuring in avertebrate subject an index of porosity and non-connectivity of a bonedisposed within a body part, the apparatus comprising:(a) first andsecond transducers, at least one of the transducers employing avibrating element that is sufficiently small as to cause the at leastone transducer, if driven by the signal generator, to produce anacoustical output, into the body part, that is substantially like thatof a point source; (b) a mounting arrangement for mounting thetransducers in spaced relationship with respect to the bone; (c) asignal generator, in communication with the first transducer, forcausing the first transducer to produce an acoustic signal, havingenergy distributed over a frequency range, that is propagated into thesubject and received by the second transducer along a first path thatincludes the bone; and (d) a signal processor, in communication with thesecond transducer, for providing a single measurement that is a functionof at least one of spectral or temporal components of a portion, up tothe whole mount thereof, of the acoustic signal received by the secondtransducer.
 19. An apparatus according to claim 18, wherein the functionincludes a weighted sum of spectral components of a portion of thesignal received by the second transducer.
 20. An apparatus according toclaim 18, wherein the function includes a measure of the shape of theHilbert envelope of a portion of the signal received by the secondtransducer.
 21. An apparatus according to claim 18, wherein the functionincludes a measure of the shape of an autoregressive moving averagespectral estimation function of a portion of the signal received by thesecond transducer.
 22. An apparatus according to claim 18, wherein thefunction includes a measure of the variability of the Hilbert frequencyfunction of a portion of the signal received by the second transducer.23. An apparatus according to claim 18, wherein the function includes ameasure of the average Hilbert frequency function of an early portion ofthe signal received by the second transducer.
 24. An apparatus accordingto claim 18, wherein the function includes a weighted sum of spectralcomponents, determined using a short-time Fourier transform, anddetermined at successive intervals, of the signal received by the secondtransducer, wherein the successive weighted sums associated withsuccessive intervals are themselves formed into a weighted sum.
 25. Anapparatus according to claim 18, wherein the function includes a measureof the group delay of a portion of the signal received by the secondtransducer.
 26. An apparatus according to claim 18, wherein the functionincludes a measure of the normalized ratio of narrow-band energy tobroad-band energy of a portion of the signal received by the secondtransducer.
 27. An apparatus for externally determining in a vertebratesubject an index of porosity and non-connectivity of a bone disposedwithin a body part, the apparatus comprising:(a) first and secondtransducers; (b) a mounting arrangement for mounting the transducers inspaced relationship with respect to the bone; (c) a signal generator, incommunication with the first transducer, for causing the firsttransducer to produce an acoustic signal, having energy distributed overa frequency range, that is propagated into the subject and received bythe second transducer along a first path that includes the bone; (d) asignal processor, in communication with the second transducer, forproviding a single measurement that is a function of at least one ofspectral or temporal components of a portion, up to the whole amountthereof, of the signal received by the second transducer; wherein aselected one of the transducers employs a vibrating element that issufficiently small as to cause the selected transducer, if driven by thesignal generator, to produce an acoustical output, into the body part,that is substantially like that of a point source.
 28. An apparatusaccording to claim 27, wherein the selected transducer employs aresonating element that has a diameter of less than 2 cm.
 29. Anapparatus according to claim 27, wherein the selected transducer employsa resonating element that has a diameter of less than 1 cm.
 30. Anapparatus according to claim 27, wherein each of the transducers employsa resonating element that has a diameter of less than 1 cm.
 31. A methodfor externally determining in a vertebrate subject an index of porosityand non-connectivity of a bone disposed within a body part, the methodcomprising:(a) providing first and second transducers, wherein aselected one of the transducers employs a vibrating element that issufficiently small as to cause the selected transducer, if driven by thesignal generator, to produce an acoustical output, into the body part,that is substantially like that of a point source; (b) mounting thetransducers in spaced relationship with respect to the bone; (c)utilizing a signal generator, in communication with the firsttransducer, to cause the first transducer to produce an acoustic signal,having energy distributed over a frequency range, that is propagatedinto the subject and received by the second transducer along a firstpath that includes the bone; and (d) processing the signal received bythe second transducer so as to provide a single measurement that is afunction of at least one of spectral or temporal components of aportion, up to the whole amount thereof, of the signal received by thesecond transducer.
 32. A method according to claim 31, wherein, in step(a), each of the transducers employs a vibrating element that issufficiently small as to cause the such transducer, if driven by thesignal generator, to produce an acoustical output, into the body part,that is substantially like that of a point source.